|
6007
|
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
|
|
Full Idea:
The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person.
|
|
From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
|
|
A reaction:
Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976).
|
|
6008
|
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
|
|
Full Idea:
The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap.
|
|
From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
|
|
A reaction:
(also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213).
|
|
14248
|
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
|
|
Full Idea:
A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
|
|
From:
Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
|
|
A reaction:
I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
|
|
5845
|
Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
|
|
Full Idea:
Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'.
|
|
From:
Xenophon (Symposium [c.391 BCE], 3.5)
|
|
A reaction:
This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue
|